Cumulative formation of response surface and its use in reliability analysis

Das, P.K.; Zheng, Yuehong

doi:10.1016/s0266-8920(99)00030-2

Cited by 134 publications

(55 citation statements)

References 7 publications

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“…Such surrogate functions have been considered in context of quadratic response surfaces by Kim and Na [25] and Das and Zheng [8], in context of support vector machines by Hurtado [23], Deheeger and Lemaire [10] and Bourinet et al [5], in context of neural networks by Papadrakakis and Lagaros [40], and in context of kriging and related concepts by Santner et al [45] (see Sects. 3.3 and 3.4 with further references therein), Kaymaz [24] and Bichon et al [4].…”

Section: Nonparametric Quantile Estimation Using Importance Samplingmentioning

confidence: 99%

Recent Results on Nonparametric Quantile Estimation in a Simulation Model

Krzyżak¹

2015

Studies in Computational Intelligence

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We present recent results on nonparametric estimation of a quantile of distribution of Y given by a simulation model Y = m(X ), where m : R d → R is a function which is costly to compute and X is a R d -valued random variable with given density. We argue that importance sampling quantile estimate of m(X ), based on a suitable estimate m n of m achieves better rate of convergence than the estimate based on order statistics alone. Similar results are given for Robbins-Monro type recursive importance sampling and for quantile estimation based on surrogate model.

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Section: Nonparametric Quantile Estimation Using Importance Samplingmentioning

confidence: 99%

Recent Results on Nonparametric Quantile Estimation in a Simulation Model

Krzyżak¹

2015

Studies in Computational Intelligence

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“…Das and Zheng [13] proposed a cumulative response surface. A first surface is formed in a linear response for determining the point of design.…”

Section: Different Approaches To Modeling Responsementioning

confidence: 99%

Adaptive response surface by kriging using pilot points for structural reliability analysis

Nassim¹

2013

IOSR-JMCE

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“…Kim and Na (1997) proposed a sequential approach to the surrogate model where the gradient projection method is used to ensure that the sampling points are located near the failure surface. Das and Zheng (2000) proposed an improved surrogate model and applied it to reliability analysis of a stiffened plate structure. Guan and Melchers (2001) evaluated the effect of surrogate model parameter variation on reliability.…”

Section: Review On Surrogate Models In Reliability Analysismentioning

confidence: 99%

Doubly weighted moving least squares and its application to structural reliability analysis

Wang

Kim

2011

Struct Multidisc Optim

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In this paper, we proposed a two-stage hybrid reliability analysis framework based on the surrogate model, which combines the first-order reliability method and Monte Carlo simulation with a doubly-weighted moving least squares (DWMLS) method. The first stage consists of constructing a surrogate model based on DWMLS. The weight system of DWMLS considers not only the normal weight factor of moving least squares, but also the distance from the most probable failure point (MPFP), which accounts for reliability problems. An adaptive experimental design scheme is proposed, during which the MPFP is progressively updated. The approximate values and sensitivity information of DWMLS are chosen to determine the number and location of the experimental design points in the next iteration, until a convergence criterion is satisfied. In the second stage, MCS on the surrogate model is then used to calculate the probability of failure. The proposed method is applied to five benchmark examples to validate its accuracy and efficiency. Results show that the proposed surrogate model with DWMLS can estimate the failure probability accurately, while requiring fewer original model simulations. KeywordsDoubly weighted moving least squares · Surrogate model · Two-stage hybrid method · Adaptive experimental design · Structural reliability analysis · Latin hypercube design Nomenclature n number of input random variables N number of experimental points x vector of input random variables β reliability index β H L reliability index by Hasofer-Lind algorithm μ mean σ standard deviation g(X) limit state function g(X) approximate limit state function/ response surface function X add new added experimental points in any iteration MLS moving least square DWMLS doubly weighted moving least square SVR support vector regression ANN artificial neural networks MPFP most probable failure point MCS Monte Carlo Simulation FORM first order reliability method SORM second order reliability method H-L Hasofer-Lind algorithm RSM response surface method LHD Latin hypercube design FEA finite element analysis CFD computational fluid dynamics COV coefficient of variation UDR Univariate Dimension-Reduction MPP-UDR Most probable point based UDR SGI Sparse Grid Interpolation 70 J. Li et al.

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Cumulative formation of response surface and its use in reliability analysis

Cited by 134 publications

References 7 publications

Recent Results on Nonparametric Quantile Estimation in a Simulation Model

Recent Results on Nonparametric Quantile Estimation in a Simulation Model

Adaptive response surface by kriging using pilot points for structural reliability analysis

Doubly weighted moving least squares and its application to structural reliability analysis

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